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9-3 Sample Spaces
Warm Up
1. A dog catches 8 out of 14 flying disks
thrown. What is the experimental probability
that it will catch the next one? 4
7
2. If Ted popped 8 balloons out of 12 tries,
what is the experimental probability that he
will pop the next balloon? 2
3
9-3 Sample Spaces
Because you can roll the
numbers 1, 2, 3, 4, 5, and
6 on a number cube, there
are 6 possible outcomes.
Together, all the possible
outcomes of an experiment
make up the sample
space.
You can make an organized list to show all possible
outcomes of an experiment.
9-3 Sample Spaces
One bag has a red tile, a blue tile, and a
green tile. A second bag has a red tile and
a blue tile. Vincent draws one tile from
each bag. What are all the possible
outcomes? How many outcomes are in the
sample space?
9-3 Sample Spaces
1
Understand the Problem
Rewrite the question as a statement.
Find all the possible outcomes of drawing
one tile from each bag, and determine the
size of the sample space.
List the important information:
•
•
There are two bags.
•
One bag has a red tile, a blue tile, and a
green tile.
•
The other bag has a red tile and a blue tile.
9-3 Sample Spaces
2
Make a Plan
You can make an organized list to show all
possible outcomes.
9-3 Sample Spaces
3
Solve
Bag 1 Bag 2
R
R
R
B
B
R
B
B
G
R
G
B
Let R = red tile,
B = blue tile, and
G = green tile.
Record each possible outcome.
The possible outcomes are RR, RB, BR, BB, GR,
and GB. There are six possible outcomes in the
sample space.
9-3 Sample Spaces
4
Look Back
Each possible outcome that is recorded in
the list is different.
9-3 Sample Spaces
Darren has two bags of marbles. One has a
green marble and a red marble. The second
bag has a blue and a red marble. Darren draws
one marble from each bag. What are all the
possible outcomes? How many outcomes are in
the sample space?
9-3 Sample Spaces
There are 4 cards and 2 tiles in a board game.
The cards are labeled N, S, E, and W. The tiles
are numbered 1 and 2. A player randomly
selects one card and one tile. What are all the
possible outcomes? How many outcomes are
in the sample space?
9-3 Sample Spaces
Shauna spins the spinner at left and flips a
coin. Complete the tree diagram. What are all
the possible outcomes? How many outcomes
are in the sample space?
9-3 Sample Spaces
2
1
H
T
H
4
3
T
H
T
H
T
9-3 Sample Spaces
In Additional Example
1, there are three
outcomes for the first
bag and two outcomes
for the second bag.

First bag
In Additional Example 2,
there are four outcomes
for the cards and two
outcomes for the tiles. Cards

Second bag
Tiles
9-3 Sample Spaces
The Fundamental Counting Principle states
that you can find the total number of outcomes
for two or more experiments by multiplying the
number of outcomes for each separate
experiment.
9-3 Sample Spaces
Carrie rolls two 1–6 number cubes. How many
outcomes are possible?
List the number of outcomes for each separate
experiment.
Use the Fundamental Counting Principle.
9-3 Sample Spaces
Juan tosses a coin and rolls a number cube.
How many outcomes are possible?
There are two possible outcomes for the coin. There
are six possible outcomes for the number cube.
9-3 Sample Spaces
Juan rolls a number cube and spins the spinner
shown in Check It Out question 2. How many
outcomes are possible?
9-3 Sample Spaces
What are all the possible outcomes? How
many outcomes are in the sample space?
1. a three question true-false test
2. tossing four coins
3. choosing a pair of cocaptains from the
following athletes: Anna, Ben, Carol, Dan, Ed,
Fran
9-3 Sample Spaces
1. Three fair coins are tossed. What are all the
possible outcomes? How many outcomes are in the
sample space?
9-3 Sample Spaces
2. Sam tosses a coin and rolls a number cube.
What are all the possible outcomes? How many
outcomes are in the sample space?
9-3 Sample Spaces
3. Bag A contains a red, a blue, and a yellow ball.
Bag B contains a white, an orange, and a green
ball. Frederica draws one ball from each bag. What
are all the possible outcomes? How many
outcomes are in the sample space?